Algebra worksheet — GCSE Foundation

1.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

2.The point A is at (5, −3). In which quadrant does A lie?

3.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

4.Make x the subject of the formula y = x + 7.

5.Expand 2(x + 12)

6.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

7.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

8.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

9.Which of these rules generates the sequence 6, 11, 16, 21, …?

10.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

11.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

12.Make x the subject of the formula y = (x − 4)/5.

13.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

14.Solve 3x + 14 = 8x − 6

15.Solve the inequality 4x + 1 > 2x + 9.